The area of a triangle with sides of length 6 cm , 8 cm and 10 cm has to be determined.

Looking at the length of the sides notice that 6^2 + 8^2 = 36 + 64 = 100 = 10^2. This is a right triangle with perpendicular sides of length 6 and 8 cm. The area of the triangle is (1/2)*6*8 = 24 cm^2.

The area can also be derived using Heron's theorem. The area is given by `sqrt(s*(s - a)*(s -b)*(s-c))` where s is the semi-perimeter equal to `(6+8+10)/2 = 12` , a = 6, b = 8 and c = 10.

The area of the triangle is equal to `sqrt(12*6*4*2) = sqrt(576)` = 24 cm^2.